It is well known that in the quantization of certain relativistic theories such electromagnetism or relativistic string negative norm states could arise when quantizing covariantly. Acting with creation and annihilation operators over the ground state one can construct the state space. Some of these have negative norm but when we impose the constraint ghosts disappear.
For the relativistic particle I am lookng for a similar idea to construct states with negative norm, then the constraint $p^2+m^2=0$ should eliminate them. Certainly this case is different because you dont have oscilator operators but I guess that ghost should appear too. I suspect that the eigenvectors of $P_0$ could have negative norm but I haven't been able to prove it.
I was looking for reference or books treating this but nothing was found, the only book mentioning a little bit is Introduction to Superstrings and M-theory by Michio Kaku in page 29.
I would like to underline the fact that my question is not about brst quantization. Do not talk me about the ghost and antighost.
I just want to know :
(1)if eigenvectors of $P_0$ have negative norm.
(2)what states kill the constraint $p^2+m^2$. In a similar way that in string theory the virasoro constraint kills ghosts and the gauss law kills ghost photon states in electromagnetism. Note that Kaku in page 29 says that this is a "ghost killing constraint" in what he calls Gupta-Bleuler quantization.